A Mathematical Model for Chemo-mechanically Induced Collective Cell Motility on Planar Elastic Substrates

Cells interact with mechanical and chemical environmental cues, such as mechanical cues from other cells and chemical signals from growth factors. The current study aims to develop a mathematical model for combined chemically and mechanically induced collective cell motility on planar substrates. In this model, an extension of a previous model simulates cell motility induced by strain energy density gradients in the planar substrate originating from cellular traction forces is presented to capture the effect of a growth factor gradient and describe chemo-mechanically induced deterministic collective cell motility on planar elastic substrates. Green’s function and Duhamel’s principle are used to solve the diffusion equation that describes the distribution of a growth factor and to represent chemo-mechanically induced deterministic collective cell motility on planar elastic substrates. The migratory displacement and velocity of a single cell towards the growth factor source on the elastic substrate are demonstrated for varying growth factor production and diffusion rates. Chemically induced motility of 25 cells towards the growth factor source is predicted for different growth factor production and diffusion rates. Chemo-mechanical cues with varying growth factor production and diffusion rates are explored for the motility of four cells and one motile cell in the presence of one stationary cell. The developed model describes the chemo-mechanically induced motility of individual cells on planar substrates. The model provides valuable information for in vivo or in vitro due to its suitability for extension to other chemical source shapes, mobilized sources, many sources, and soluble concentration gradients.